Stan Model
## S4 class stanmodel 'DE-modelSpec' coded as follows:
## data {
## int<lower=0> N; // num observations
## int<lower=0> ni; // num items
## int<lower=0> ns; // num subjects
## int<lower=0> nsi; // num subject-item combos
## int<lower=0> si_lookup[ns, ni]; // lookup table for sparsely coded subject-item offsets
## int<lower=0> nt; // num trials
## int<lower=0> nc; // num strategies
## real<lower=0> y[N]; // log RT
## int<lower=0> strategy[N]; // strategy for a given obs
## int<lower=0> item[N]; // item for a given obs
## int<lower=0> subject[N]; // subject for a given obs
## int<lower=0> trial[N]; // trial for a given obs
## }
##
## parameters {
## real A; // = log_A, to be exponentialted later
## real A_es[ns];
## real A_ei[ni];
## //real A_esi[ns,ni];
## real A_esi[nsi];
## real<lower=0> sigma_A_ei;
## real<lower=0> sigma_A_es;
## real<lower=0> sigma_A_esi;
##
## real B; // = log_B, to be exponentialted later
## real B_es[ns];
## real B_ei[ni];
## //real B_esi[ns,ni];
## real B_esi[nsi];
## real<lower=0> sigma_B_ei;
## real<lower=0> sigma_B_es;
## real<lower=0> sigma_B_esi;
##
## real T;
## real T_es[ns];
## real T_ei[ni];
## //real T_esi[ns,ni];
## real T_esi[nsi];
## real<lower=0> sigma_T_ei;
## real<lower=0> sigma_T_es;
## real<lower=0> sigma_T_esi;
##
## real R;
## real R_es[ns];
## real R_ei[ni];
## //real R_esi[ns,ni];
## real R_esi[nsi];
## real<lower=0> sigma_R_ei;
## real<lower=0> sigma_R_es;
## real<lower=0> sigma_R_esi;
##
## // add sigma variability
##
## real<lower=0> sigma;
## }
##
## transformed parameters {
## real y_hat[N];
## real Alpha;
## real Beta;// = B + B_es[subject[i]] + B_ei[item[i]] + B_esi[subject[i], item[i]];
## real log_Rate;// = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[subject[i], item[i]];
## real log_Tau;// = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[subject[i], item[i]];
##
## for(i in 1:N){
## Alpha = exp(A + A_es[subject[i]] + A_ei[item[i]] + A_esi[si_lookup[subject[i], item[i]]]);
## Beta = exp(B + B_es[subject[i]] + B_ei[item[i]] + B_esi[si_lookup[subject[i], item[i]]]);
## log_Rate = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[si_lookup[subject[i], item[i]]];
## log_Tau = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[si_lookup[subject[i], item[i]]];
## // Tau = exp(Tau*Rate)-2; // old transformed version
## // print(log_Alpha[i]);
## // print(log_Beta[i]);
## // print(Tau[i]);
## // print(Rate[i]);
## // print(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i]));
## // print(log(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i])));
## // print("");
## y_hat[i] = log(Alpha + Beta * (exp(log_Tau) + 1)/(exp(log_Tau) + exp(exp(log_Rate)*trial[i])));
## // this resulted in no delayed start ever... : log(exp(log_Alpha) + (exp(log_Beta) * (exp(log_Tau) + 1) /(exp(log_Tau) + exp(log_Rate)*trial[i])));
## // **old transformed version** log(exp(log_Alpha) + exp(log_Beta) * (Tau+1) / (Tau + trial[i]^Rate));
## // go back to original version, but constrain Tau, Rate to be positive
## }
## }
##
## model {
## sigma ~ exponential(.1);
##
## A ~ normal(0, 6); // set as overall mean and sd of data
## B ~ normal(8, 5); // set as mean, sd for retrieval trials
## T ~ normal(5, 10); // was centered on 0
## R ~ normal(-1, 2);
##
## sigma_A_es ~ exponential(1);
## sigma_A_ei ~ exponential(1);
## sigma_A_esi ~ exponential(1);
##
## sigma_B_es ~ exponential(1);
## sigma_B_ei ~ exponential(1);
## sigma_B_esi ~ exponential(1);
##
## sigma_R_es ~ exponential(1);
## sigma_R_ei ~ exponential(1);
## sigma_R_esi ~ exponential(1);
##
## sigma_T_es ~ exponential(1);
## sigma_T_ei ~ exponential(1);
## sigma_T_esi ~ exponential(1);
##
## A_es ~ normal(0, sigma_A_es);
## A_ei ~ normal(0, sigma_A_ei);
## A_esi ~ normal(0, sigma_A_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // A_esi[i,j] ~ normal(0, sigma_A_esi);
## // }
##
## B_es ~ normal(0, sigma_B_es);
## B_ei ~ normal(0, sigma_B_ei);
## B_esi ~ normal(0, sigma_B_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // B_esi[i,j] ~ normal(0, sigma_B_esi);
## // }
##
## R_es ~ normal(0, sigma_R_es);
## R_ei ~ normal(0, sigma_R_ei);
## R_esi ~ normal(0, sigma_R_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // R_esi[i,j] ~ normal(0, sigma_R_esi);
## // }
##
## T_es ~ normal(0, sigma_T_es);
## T_ei ~ normal(0, sigma_T_ei);
## T_esi ~ normal(0, sigma_T_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // T_esi[i,j] ~ normal(0, sigma_T_esi);
## // }
##
## y ~ normal(y_hat, sigma);
## }
## generated quantities {
## vector[N] logLik;
## for(n in 1:N){
## logLik[n] = normal_lpdf(y[n] | y_hat[n], sigma);
## }
## }
